Physical Models of an Elevator - version 0.5 - concept - 2025-08-16

Oct 23, 2026

An elevator is modeled as a simple physical system to explain design-relevant behavior through kinematics and energy-consumption considerations. The material presents low-level motion models, starting from a trivial setup and extending through first- and second-order corrections using acceleration and jerk limits. It also connects model outputs—time, velocity, and acceleration—to constraints for passengers’ comfort and motor/control considerations, including example parameter choices for reaching the top floor.

LanguageEnglish

CategoryTechnology

FormatPDF

Pages40

Reading Time1 h 41 min

AccessFree to download

Abstract

Distribution and Status

1st Order Model

Coarse 2nd Order Correction

Modeling Goals and Abstraction Levels

Elevator Motion Definitions

Expected Parameter Values

Time to Reach Top Floor Models

0th Order Model

1st Order Model

Physical Models of an Elevator by Gerrit Muller University of South-Eastern Norway USN-SE e-mail: [gaudisite@gmail.com](gaudisite@gmail.com) [www.gaudisite.nl](www.gaudisite.nl) Abstract An elevator is used as a simple system to model a few physical aspects. We will show simple kinematic models and we will consider energy consumption. These low level models are used to understand (physical) design considerations. Elsewhere we discuss higher level models, such as use cases and throughput, which complement these low level models. Distribution This article or presentation is written as part of the Gaudí project. The Gaudí project philosophy is to improve by obtaining frequent feedback. Frequent feedback is pursued by an open creation process. This document is published as intermediate or nearly mature version to get feedback. Further distribution is allowed as long as the document remains complete and unchanged. August 16, 2025 status: concept version: 0.5 | 1st order model

S(ta) = ~~ ~~12 * amax * ta2
ta =√( S(ta)/ (0 .5*amax))
tone floor = 2 ta =2√( S(ta)/ (0 .5*amax)) v(ta) = amta v(ta) ~= 1.2* 1.6 ~= 1.9 m/s

input data
S0 = 0m Sone floor = 3mvmax = 2.5 m/s
amax = 1.2 m/s2 (up) jmax = 2.5 m/s3
tone floor ~=
2√( 1 .5 / (0 .5* 1.2)) ~= 2 * 1.6s ~= 3s | | --- | | coarse 2nd order correction

v
tone floor = 2 ta + 2 tj
tj ~= 0.5s

tj ta ta tj t

tone floor~= 2* 1.6 + 2*0.5 ~= 4s | To understand the need for · various views, e.g. physical, functional, performance · mathematical models · quantified understanding · assumptions (when input data is unavailable yet) and later validation · various visualizations, e.g. graphs · understand and hence model at multiple levels of abstraction · starting simple and expanding in detail, views, and solutions gradually, based on increased insight To see the value and the limitations of these conceptual models To appreciate the complementarity of conceptual models to other forms of modeling, e.g. problem specific models (e.g. structural or thermal analysis) , SysML models, or simulations Physical Models of an Elevator 3 Gerrit Muller version: 0.5 August 16, 2025 EPMlearningGoals warning This presentation starts with a trivial problem. Have patience! Extensions to the trivial problem are used to illustrate many different modeling aspects. Feedback on correctness and validity is appreciated building | top floor | | | | | --- | --- | --- | --- | | | | | | | elevator | | | | | | | | | | | | | | 40 m inhabitants want to reach their destination fast and comfortable building owner and service operator have economic constraints: space, cost, energy, . .. St = position at time t vt = velocity at time t at = acceleration at time tjt = jerk at time t v = dS dt a = dv dt j = ~~ ~~ddat~~ ~~ Position in case of uniform acceleration: St = S0 + v0t + ~~ ~~12 a0t2 building | top floor | | | | --- | --- | --- | | elevator | | | | | | | | | | | 40 m What values do you expect or prefer for these quantities? Why? ttop floor = time to reach top floor v max = maximum velocity a max = maximum acceleration j max = maximum jerk building | top floor | | | | | --- | --- | --- | --- | | | | | | | elevator | | | | | | | | | | | | | | 40 m Google "elevator" and "jerk" : ttop floor ~= 16 s 12% of gravity; weight goes up vmax ~= 2.5 m/s amax ~= 1.2 m/s2 (up) relates to motor design and energy consumption jmax ~= 2.5 m/s3 ~~ ~~ relates to control design humans feel changes of forces high jerk values are uncomfortable numbers from: [http://www.sensor123.com/vm_eva625.htm](http://www.sensor123.com/vm_eva625.htm) CEP Instruments Pte Ltd Singapore input data S0 = 0m St = 40mv max = 2.5 m/s a max = 1.2 m/s2 (up) j max = 2.5 m/s3 elementary formulas v = dS dt a = dv dt j = ~~

FAQs

What physical aspects does the document model for an elevator?

It models a few physical aspects using kinematic models and examines energy consumption. It focuses on how motion constraints influence design considerations.

What do the document’s main motion quantities represent?

S(t) is position at time t, v(t) is velocity, a(t) is acceleration, and j(t) is jerk. These are linked by v = dS/dt, a = dv/dt, and j = d a/dt.

How is the time to reach the top floor estimated in the 0th and 1st order models?

The 0th order model assumes constant velocity, using ttop floor = Stop floor / vmax. The 1st order model assumes constant acceleration, using ttop floor = ta + tv + ta, derived from relations for the distance covered during acceleration and the remaining distance at linear velocity.

Oct 23, 2026

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